6. Thermodynamics and Kinetics

The alkyl carbocation is estimated to be 15 kcal/mol more stable than the alkenyl carbocation. If this is also the difference in the energies of the transition state leading to each, what is the expected rate difference? 

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Using Equation 5.8, calculate the difference in transition state energies that lead to the rate differences shown in Figure 24.35.

Draw a reaction coordinate diagram, making sure to label reactants (R), products (P), intermediates (I), transition states (‡), activation energies ( E_a) , and ∆G°, for each of the following.

(b) an exothermic, two-step reaction where the second step is rate-determining

Draw a reaction coordinate diagram, making sure to label reactants (R), products (P), intermediates (I), transition states (‡), activation energies ( E_a) , and ∆G°, for each of the following.

(c) a slightly endothermic, three-step reaction where the first step is rate-determining

Draw a reaction-energy diagram for the propagation steps of the free-radical addition of HBr to isobutylene. Draw curves representing the reactions leading to both the Markovnikov and the anti-Markovnikov products. Compare the values of ∆Gº and Ea and for the rate-limiting steps, and explain why only one of these products is observed.

Draw a reaction coordinate diagram for a reaction in which

a. the product is thermodynamically unstable and kinetically unstable.

b. the product is thermodynamically unstable and kinetically stable.

Draw a reaction coordinate diagram for a two-step reaction in which the first step is endergonic, the second step is exergonic, and the overall reaction is endergonic. Label the reactants, products, intermediates, and transition states.

The acid dissociation constant (K_a) for loss of a proton from cyclohexanol is 1 × 10^–16.

a. Draw a reaction coordinate diagram for loss of a proton from cyclohexanol.

The reaction of tert-butyl chloride with methanol

is found to follow the rate equation

rate = k_r[(CH₃)₃C—Cl]

b. What is the kinetic order with respect to methanol?

Under certain conditions, the bromination of cyclohexene follows an unusual rate law:

c. What is the overall kinetic order?

The following reaction is a common synthesis used in the organic chemistry laboratory course.

When we double the concentration of methoxide ion (CH₃O^–), we find that the reaction rate doubles. When we triple the concentration of 1-bromobutane, we find that the reaction rate triples.

a. What is the order of this reaction with respect to 1-bromobutane? What is the order with respect to methoxide ion? Write the rate equation for this reaction. What is the overall order?

Deuterium (D) is the hydrogen isotope of mass number 2, with a proton and a neutron in its nucleus. The chemistry of deuterium is nearly identical to the chemistry of hydrogen, except that the C―D bond is slightly stronger than the C―H bond by 5.0 kJ/mol (1.2 kcal/mol). Reaction rates tend to be slower when a C―D bond (as opposed to a C―H bond) is broken in a rate-limiting step.

This effect, called a kinetic isotope effect, is clearly seen in the chlorination of methane. Methane undergoes free-radical chlorination 12 times as fast as tetradeuteriomethane (CD₄).

b. Monochlorination of deuterioethane (C₂H₅D) leads to a mixture containing 93% C₂H₄DCl and 7% C₂H₅Cl. Calculate the relative rates of abstraction per hydrogen and deuterium in the chlorination of deuterioethane.

Treatment of tert-butyl alcohol with concentrated HCl gives tert-butyl chloride.

When the concentration of H⁺ is doubled, the reaction rate doubles. When the concentration of tert-butyl alcohol is tripled, the reaction rate triples. When the chloride ion concentration is quadrupled, however, the reaction rate is unchanged. Write the rate equation for this reaction.

When a small piece of platinum is added to a mixture of ethene and hydrogen, the ­following reaction occurs:

Doubling the concentration of hydrogen has no effect on the reaction rate. Doubling the concentration of ethene also has no effect.

b. Write the unusual rate equation for this reaction.

c. Explain this strange rate equation, and suggest what one might do to accelerate the reaction.

(a) On a reaction coordinate diagram, show why a general, one-step reaction is faster when a catalyst is employed.

(b) Why does a catalyst often allow a reaction to proceed at lower temperatures?